statsmodels.stats.power.tt_solve_power(effect_size=None, nobs=None, alpha=None, power=None, alternative='two-sided')

solve for any one parameter of the power of a one sample t-test

for the one sample t-test the keywords are:

effect_size, nobs, alpha, power

Exactly one needs to be None, all others need numeric values.

This test can also be used for a paired t-test, where effect size is defined in terms of the mean difference, and nobs is the number of pairs.


Standardized effect size.The effect size is here Cohen’s f, square root of “f2”.

nobsint or float

sample size, number of observations.

alphafloat in interval (0,1)

significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true.

powerfloat in interval (0,1)

power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true.

alternativestr, ‘two-sided’ (default) or ‘one-sided’

extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. ‘one-sided’ assumes we are in the relevant tail.


The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters.


Cache of the result of the root finding procedure for the latest call to solve_power, mainly for debugging purposes. The first element is the success indicator, one if successful. The remaining elements contain the return information of the up to three solvers that have been tried.


The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses brentq with a prior search for bounds. If this fails to find a root, fsolve is used. If fsolve also fails, then, for alpha, power and effect_size, brentq with fixed bounds is used. However, there can still be cases where this fails.

Last update: Dec 14, 2023